*Astron. Astrophys. 348, 524-532 (1999)*
## 4. The *R*() relation of [M/H] ZAMS dwarfs
For stars of given age and metallicity, theory provides the radius
as a function of absolute magnitude, e.g.
. In the present context this follows
from the fact that the models yield
as a function of which transforms
Eq. (6) into
()
and Eq. (2) into *R*().
Fig. 3a shows the observed radii of YY Gem (mean component) and the
eight YD, four old disk (OD), and four halo (H) M-dwarfs of L96 along
with the BCAH98 model radii for solar-composition ZAMS stars (solid
curve, see also Fig. 1 of Paper I). There is no obvious difference
between the radii of YD and OD stars in this rather restricted sample.
The two faint H stars show the expected smaller radii. This is
consistent with the small metallicity dependence of the
*R*() BCAH98 models which can
approximately be expressed by
log
per 1 dex reduction of [M/H] relative to solar (BCAH98). On the
average, the L96 radii of the YD/OD stars exceed the [M/H] = 0 ZAMS
model radii by 2% (Paper I) which is within the systematic
uncertainties of the L96 radii. These model radii (solid curve) can be
represented reasonably well by a third-order polynomial in
which we adjust slightly, by
, to nominally fit the L96 radii
(dot-dashed curve in Fig. 3a)
We accept Eq. (7) as representative of ZAMS stars with near-solar
or slightly reduced metallicities (kinematic classes YD and OD). Note
that radii for stars fainter than
are
still uncertain because dust formation is not accounted for in the
BCAH98 models
Stellar radii may be estimated either from a Barnes-Evans type
relation as Eq. (6) together with Eq. (2) or directly from the
*R*() relation in Eq. (7). The
former depends weakly on gravity but distinctly on metallicity, while
the latter depends weakly on metallicity and strongly on gravity and,
therefore, requires knowledge of the evolutionary status.
The different metallicity dependencies of the two approaches arise
because reference is taken to a colour in one case and directly to the
abolute magnitude in the other. The difference in the approaches
becomes more obvious when combining Eqs. (2), (6), and (7) to yield
the colour-magnitude relation vs.
for ZAMS stars of near-solar
metallicity
(Fig. 3b, dot-dashed curve). Eq. (8) closely fits the L96 YD stars
(encircled dots) which is as expected because Eqs. (6) and (7) fit
these stars, too. Although Eq. (7) is approximately valid also for OD
stars with slightly reduced metallicity, Eq. (6) and Eq. (8) are not.
At the *same * , stars of lower
metallicity (open points, triangles in Fig. 3b) are bluer. They have
nearly unchanged and radii, however,
because the metallicity dependence of the colour in Fig. 3b and the
metallicity dependence of
in
Fig. 2b compensate approximately. This implies that application of the
Barnes-Evans relations in Fig. 2 requires knowledge of the metallicity
of the respective stars.
© European Southern Observatory (ESO) 1999
Online publication: July 26, 1999
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